We propose a method aimed at detecting weak, sparse signals in highly noisy three-dimensional (3D) data. 3D data sets usually combine two spatial directions x and y (e.g. image or video frame dimensions) with an additional direction λ (e.g. temporal, spectral or energy dimension). Such data most often suffer from information leakage caused by the acquisition system's point spread functions, which may be different and variable in the three dimensions. The proposed test is based on dedicated 3D dictionaries, and exploits both the sparsity of the data along the λ direction and the information spread in the three dimensions. Numerical results are shown in the context of astrophysical hyperspectral data, for which the proposed 3D model substantially improves over 1D detection approaches.

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This paper considers a "one among many" detection problem, where one has to discriminate between pure noise and one among alternatives that are known up to an amplitude factor. Two issues linked to high dimensionality arise in this framework. First, the computational complexity associated to the Generalized Likelihood Ratio (GLR) with the constraint of sparsity-one inflates linearly with , which can be an obstacle when multiple data sets have to be tested. Second, standard procedures based on dictionary learning aimed at reducing the dimensionality may suffer from severe power losses for some alternatives, thus suggesting a worst-case scenario strategy. In the case where the learned dictionary has column, we show that the exact solution of the resulting detection problem, which can be formulated as a minimax problem, can be obtained by Quadratic Programming. Because it allows a better sampling of the diversity of the alternatives, the case is expected to improve the detection performances over the case . The worst-case analysis of this case, which is more involved, leads us to propose two "minimax learning algorithms". Numerical results show that these algorithms indeed allow to increase performances over the case and are in fact comparable to the GLR using the full set of alternatives, while being computationally simpler.

This paper discusses on the design of a ridge waveguide slot antenna to be operated at the frequency of 63 GHz. The frequency is used for vehicle-to-vehicle (V2V) application. The antenna is design as structured in 5 layers of metal coated SU-8 photoresist, each at 200µm thick. The performance of the antenna is simulated using CST Microwave Studio 3D simulator. The simulation result shows that the antenna is well matched at 63 GHz with -28.7 dB return loss and a very narrow -10 dB bandwidth of 0.9 %.

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